Introduction

Electromechanical coupling is one of the fundamental mechanisms underlying
the functionality of many materials. These include inorganic macro-molecular
materials, such as piezo- and ferroelectrics, as well as many biological
systems. This application note discusses the background and principles of piezoresponse
force microscopy (PFM) measurements using the MFP-3D™ AFM
and Cypher™
AFM from Asylum Research.

Background

The functionality of systems ranging from non-volatile computer memories and
micro electromechanical systems to electromotor proteins and cellular membranes
are ultimately based on the intricate coupling between electrical and mechanical
phenomena. The applications of electromechanically active materials include
sonar, ultrasonic and medical imaging, sensors, actuators, and energy harvesting
technologies. In the realm of electronic devices, piezoelectrics are used as
components of RF filters and surface-acoustic wave (SAW) devices. The ability of
ferroelectric materials to switch polarization orientation - and maintain
polarization state in a zero electric field - has lead to emergence of concepts
of non-volatile ferroelectric memories and data storage devices.
Electromechanical coupling is the basis of many biological systems, from hearing
to cardiac activity. The future will undoubtedly see the emergence, first in
research labs and later in industrial settings, of the broad arrays of
piezoelectric, biological and molecular-based electromechanical systems.
Progress along this path requires the ability to image and quantify
electromechanical functionalities on the nanometer and molecular scale (Figures
1 and 2). Areas such as nanomechanics and single-molecule imaging and force
measurements have been enabled by the emergence of microscopic tools such as
nanoindentation and protein unfolding spectroscopy.

Similarly, the necessity for probing electromechanical functionalities has
led to the development of PFM as a tool for local nanoscale imaging, spectroscopy, and
manipulation of piezoelectric and ferroelectric materials.

Principles of Piezoresponse Force Microscopy

Basics

PFM
measures the mechanical response when an electrical voltage is applied to the
sample surface with a conductive tip of an AFM. In response to the electrical
stimulus, the sample then locally expands or contracts as shown in Figure 3.

Figure 3. Depiction of PFM operation. The sample deforms
in response to the applied voltage. This, in turn, causes the cantilever to
deflect, which can then be measured and interpreted in terms of the
piezoelectric properties of the sample. Image courtesy S. Jesse, ORNL.

When the tip is in contact with the surface and the local piezoelectric response
is detected as the first harmonic component of the tip deflection, the phase
φ, of the electromechanical response of the surface yields information on
the polarization direction below the tip. For c- domains (polarization
vector oriented normal to the surface and pointing downward), the application
of a positive tip bias results in the expansion of the sample, and surface oscillations
are in phase with the tip voltage, φ = 0. For c+ domains, the
response is opposite and φ = 180°.

Detection of the lateral components of tip vibrations provides information on
the in-plane surface displacement, known as lateral PFM. A
third component of the displacement vector can be determined by imaging the same
region of the sample after rotation by 90°. Provided that the vertical and
lateral PFM signals are properly calibrated, the complete
electromechanical response vector can be determined, an approach referred to as
vector PFM. Finally, electromechanical response can be probed as a
function of dc bias of the tip, providing information on polarization switching
in ferroelectrics, as well as more complex electrochemical and electrocapillary
processes.

PFM
requires detection of small tip displacements induced by relatively high
amplitude, high frequency voltages measured at the same frequency as the drive.
Any instrumental crosstalk between the drive and the response will result in a
virtual PFM background that can easily be larger than the PFM
response itself, especially for weak piezo materials. Minimizing crosstalk
between the driving voltage and the response imposes a number of serious
engineering limitations on the microscope mechanics and electronics. In the
past, significant post-factory modifications were required to decouple the drive
and response signals. Asylum's PFM uses a unique proprietary design of the head and
the high voltage sample holder to eliminate drive crosstalk.

Piezo Effect

The relationship between the strain and the applied electric field (often
referred to as the "inverse piezo effect") in piezoelectric materials is
described by a rank-3 tensor. The most important component of this tensor for
typical "vertical" PFM is the d33 component, since it couples directly
into the vertical motion of the cantilever. The voltage applied to the tip is

resulting in piezoelectric strain in the material that causes cantilever
displacement

due to piezoelectric effect. When the voltage is driven at a frequency well
below that of the contact resonance of the cantilever, this expression
becomes

where we have implicitly assumed d33 depends on the polarization
state of the material. From this last equation and from Figure 3, the magnitude
of the oscillating response is a measure of the magnitude of d33 and
the phase is sensitive to the polarization direction of the sample.

NOTE: In reality, the d33 component in Equation 3 is an
"effective" d33 that depends on the contribution from other tensor
elements and on the crystallographic and real space orientation of the piezo
material, as well as details of the tip-sample contact.

Typical values for d33 range from 0.1pm/V for weak piezo materials
to 500pm/V for the strongest. Table 1 shows a listing of representative
values.

Table 1

Material

Application

d33,pm/V
*1

Coercive bias (for local switching)
*2

Breakdown voltage/onset of conductivity
*3

Bulk Materials

PZT ceramics

Actuators and transducers

100 - 500

10V - 1kV

N/A

LiNbO3 single crystals

Electro-optical devices

10 - 20

10V - 1kV

N/A

Quartz

Balances, frequency standards

3

N/A

N/A

Polar semiconductors

RF devices, switches

0.1 - 2

N/A

N/A

Calcified tissues

0.5 - 3

N/A

N/A

Collagen

0.5 - 3

N/A

N/A

Thin Films and Capacitor Structures

1 - 5 micron PZT

Capacitors

10 - 30

1 - 100

100

~ 100 - 300 nm PZT

FeRAM elements

3 - 10

1 - 10

10 - 20

30 - 100 nm BiFeO3

FeRAM

3 - 10

1 - 10

10 - 20

Ultrathin Films

1 - 5 nm BiFeO3

Tunneling barriers

1- 10

1 - 5

10 (can be below switching voltage in air)

10 nm PVDF

Actuators

20

2 - 5

10

*1. The PFM signal is given by Equation 6,
A=d33VacQ where d33 is material property,
Vac is driving voltage, and Q is the quality factor. Q = 1 for low
frequency PFM, and Q = 20-100 if resonance enhancement (DRFT or BE) method is
used. Vac is limited by material stability and polarization
switching. The microscope photodetector sensitivity, thermal noise and shot
noise impose the limit A > 30pm. The ultimate limit is A = thermal
noise.*2. Quantitative spectroscopic measurements require probing bias to be
one to two orders of magnitude smaller than coercive bias, limiting the voltage
amplitude.*3. Measurements are not possible above this limit due to sample
and tip degradation.

As mentioned above, the direction of sample polarization determines the sign
of the response. Figure 4 demonstrates this idea. If the polarization is
parallel and aligned with the applied electric field, the piezo effect will be
positive, and the sample will locally expand. If the local sample polarization
is anti-parallel with the applied electric field, the sample will locally
shrink. This sign-dependent behavior means that the phase of the cantilever
provides an indication of the polarization orientation of the sample when an
oscillating voltage is applied to the sample.

Figure 4. Sign dependence of the sample strain. When the
domains have a vertical polarization that is pointed downwards and a positive
voltage is applied to the tip, the sample will locally expand. If the
polarization is pointed up, the sample will locally contract. The phase of the
measured response is thus proportional to the direction of the domain
polarization. Figure courtesy of S. Jesse, ORNL.

The relationship in Equation 1 and the values for d33 in Table 1
suggest that typical deflections for a PFM
cantilever are on the order of picometers. While the sensitivity of AFM
cantilevers is quite impressive - of the order of a fraction of an angstrom (or
tens of pm) in a 1kHz bandwidth - it also implies a very small signal-to-noise
ratio (SNR) for all but the strongest piezo materials.

Because of this small SNR, piezoelectricity is most frequently detected by a
lock-in amplifier connected to the deflection of the AFM cantilever. By
employing an oscillating electric field, low-frequency noise and drift can be
eliminated from the measurement. Until recently, PFM was usually accomplished by
researchers who modified a commercial SPM system with an external function
generator/lock in setup. As a result, in most cases, the operation frequency was
limited to <100kHz. This and the lack of sophisticated control options
precluded the use of resonance enhancement (see sections below on DART and BE)
in PFM
since typical contact resonance frequencies are >300kHz.

Piezoresponse Force Microscopy Imaging Modes

The three typical PFM imaging modes and piezoelectric lithography are briefly
described below.

Vertical PFM

In vertical PFM imaging, out-of-plane polarization is measured by
recording the tip-deflection signal at the frequency of modulation. Figure 5
shows an example image of vertical PFM for a
lead titanate film. Antiparallel domains with out-of-plane polarization can be
seen in the PFM phase image, while in-plane domains are seen in the PFM
amplitude image as yellow stripes due to the weak vertical piezoresponse
signal

Lateral PFM

Lateral PFM is a technique where the in-plane component of
polarization is detected as lateral motion of the cantilever due to bias-induced
surface shearing.

Vector PFM

In vector PFM the real space reconstruction of polarization orientation
comes from three components of piezoresponse: vertical PFM plus at
least two orthogonal lateral PFM. Figure
6 shows an example of a vector PFM image
of a barium strontium titanate film (BST), permitting qualitative inspection of
the correlation of grain size, shape and location with local polarization
orientation and domain wall character. Here, the color wheel permits
identification of the local orientation of the polarization. Regions colored as
cyan (darker blue/green) possess polarizations which are oriented predominantly
normal to the plane of the film, whereas regions that appear magenta-blue or
light green possess polarizations which are oriented predominantly within the
plane of the film. The intensity of the color map denotes the magnitude of the
response.

Lithography

For ferroelectric applications, PFM can be
used to modify the ferroelectric polarization of the sample through the
application of a bias. When the applied field is large enough (e.g. greater than
the local coercive field) it can induce ferroelectric polarization reversal.
This technique can be used to 'write' single domains, domain arrays, and complex
patterns without changing the surface topography. Figure 7 shows an example of
PFM
bit-mapped lithography where the color scale of a black and white photo was used
to control the bias voltage of the tip as it rastered over the surface and then
re-imaged in PFM mode.

Figure 7. R&D 100 logo written on a sol-gel PZT thin
film by PFM lithography. PFM phase is overlaid on top of the rendered
topography, 25µm scan. Oak Ridge and Asylum Research were awarded an R&D100
award for Band Excitation in 2008.

Spectroscopy Modes

PFM
spectroscopy refers to locally generating hysteresis loops in ferroelectric
materials. From these hysteresis loops, information on local ferroelectric
behavior such as imprint, local work of switching, and nucleation biases can be
obtained.

Understanding the switching behavior in ferroelectrics on the nanometer scale
is directly relevant to the development and optimization of applications such as
ferro-electric non-volatile random access memory (FRAM), and high-density data
storage. Multiple studies have addressed the role of defects and grain
boundaries on domain nucleation and growth, domain wall pinning, illumination
effects on the built-in potential, and domain behavior during fatigue.The
origins of the field date back to the seminal work by Landauer, who demonstrated
that the experimentally observed switching fields correspond to impossibly large
(~103 - 105 kT) values for the nucleation activation
energy in polarization switching. Resolving this 'Landauer paradox' requires the
presence of discrete switching centers that initiate low-field nucleation and
control macroscopic polarization switching. However, difficulties related to
positioning of the tip at a specific location on the surface (due in part to
microscope drift), as well as time constraints related to hysteresis loop
acquisition, limit these studies to only a few points on the sample surface,
thus precluding correlation between the material's microstructure and local
switching characteristics.

Switching Spectroscopy Mapping

A new spectroscopy technique, Switching
Spectroscopy PFM (SS-PFM), has demonstrated real-space imaging of the energy
distribution of nucleation centres in ferroelectrics, thus resolving the
structural origins of the Landauer paradox. These maps can be readily correlated
with surface topography or other microscopic techniques to provide relationships
between micro- and nanostructures and local switching behavior of ferroelectric
materials and nanostructures. Figure 8 shows how it works. In SS-PFM, a
sine wave is carried by a square wave that steps in magnitude with time. Between
each ever-increasing voltage step, the offset is stepped back to zero with the
AC bias still applied to determine the bias-induced change in polarization
distribution (e.g. the size of the switched domain). It is then possible to see
the hysteresis curve of the switching of the polarization of the surface (bottom
diagram). If the measurements are performed over a rectangular grid, a map of
the switching spectra of that surface can be obtained. Figure 9 shows an example
image of a LiNbO3 sample with the PFM signal overlaid on top. The
image was taken after switching spectroscopy. The graph shows the hysteresis
loops measured at one individual point.

As additional examples, Figure 10 shows a sol gel PZT sample where the local
switching fields were measured. After the switching spectroscopy, the area was
re-imaged. The PFM signal clearly shows five dots in the phase signal
denoting portions of the sample where the polarization was reversed during the
hysteresis measurements. Figure 11 shows SSM-PFM of
capacitor structures and Figure 12 shows an image of phase and amplitude
hysteresis loops measured at five different locations on a lead zinc niobate -
lead titanate (PZN-PTi) thin film.

Figure 10. Sol gel PZT sample where local hysteresis
loops were measured and displayed (representative phase and amplitude loops
shown at top). After the switching spectroscopy measurements, the area was
imaged, the DART amplitude (middle) and phase (bottom) are shown, 3.5µm
scan.

Figure 12. Amplitude (left) and phase (right) hysteresis
loops measured at five different locations on a PZN-PTi thin film.

Conclusion

Characterizing electromechanical responses in a variety of materials will be
crucial for understanding and improving technologies ranging from bioscience
to energy production. Scanning probe microscopy has emerged as a universal tool
for probing such structures and functionality at the nanometer scale. Asylum's
Piezoresponse Force Microscopy capabilities now allow characterization of
an endless variety of materials and devices that previously could not be measured
using conventional piezoresponse
force microscopy. Research with this new tool will enable new advancements
in many disciplines from biology to semiconductors, while yielding improvements
for ongoing work in diverse areas from data storage devices and molecular machines
to improved materials for renewable energy.

The Asylum Research Cypher™ AFMs are considered to be in a class of their own. Every design choice was guided to obtain an exceptional combination of highest resolution, integrated environmental control, fast scanning and supreme productivity.